Abstract
In this paper, we consider nonlinear Dirichlet problem driven by the p-Laplacian differential operator. Using variational methods based on the critical point theory and truncation techniques, we prove the existence of at least three nontrivial smooth solutions. The hypotheses on the nonlinearity incorporate in our framework of analysis both coercive and noncoercive problems. For the semilinear problem (p = 2), using Morse theory, we show the existence of four nontrivial smooth solutions.
Keywords: Linking sets; second eigenvalue; second deformation theorem; critical group; Poincare-Hopf formula; strong maximum principle
Received: 2008-07-29
Published Online: 2016-03-10
Published in Print: 2008-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
